Two coils A and B have mutual inductance 0.008 H . The current changes in the coil A , according to the equation I=I_m sin ω t , where I_m=5 A and ω=200 π rad s^-1 . The maximum value of the e.m.f. induced in the coil B in volt is

Correct answer: (B) 8 π. e=M dI/dt Given: M=0.008, I_m=5 ~A, ω=200 rad / s ∴ e=0.008 × I_m ω e os ω t For e=e_max , cos ω t=1 ∴ e_max =0.008 × I_m × ω =0.008 × 5 × 200 π =8 π

Q131 / 150 · MHT CET 2023 (09 May Shift 2) · Physics

Two coils A and B have mutual inductance 0.008 $\mathrm{H}$. The current changes in the coil $\mathrm{A}$, according to the equation $\mathrm{I}=\mathrm{I}_{\mathrm{m}} \sin \omega \mathrm{t}$, where $I_m=5 A$ and $\omega=200 \pi \mathrm{rad} \mathrm{s}^{-1}$. The maximum value of the e.m.f. induced in the coil B in volt is

A
$4 \pi$
Correct answer
B
$8 \pi$
C
$10 \pi$
D
$16 \pi$

Solution

$\mathrm{e}=\mathrm{M} \frac{\mathrm{dI}}{\mathrm{dt}}$ Given: $\mathrm{M}=0.008, \mathrm{I}_{\mathrm{m}}=5 \mathrm{~A}, \omega=200 \mathrm{rad} / \mathrm{s}$ $\therefore \quad \mathrm{e}=0.008 \times \mathrm{I}_{\mathrm{m}} \omega \mathrm{e} \mathrm{os} \omega \mathrm{t}$ For $\mathrm{e}=\mathrm{e}_{\max }, \cos \omega \mathrm{t}=1$ $\begin{aligned} \therefore \quad \mathrm{e}_{\max } & =0.008 \times \mathrm{I}_{\mathrm{m}} \times \omega \\ & =0.008 \times 5 \times 200 \pi \\ & =8 \pi \end{aligned}$

Hence, the correct answer is option: 'B'.

Solution

Relevant Questions